The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  0  0  1  X  1  1  X  0  X  1  X  1  1  X  X  1  1  1  1  0  X  1  X  1  1  1  0  1  1  0  1  X  1  X  1  1  X  1  1  X  1  X  1  1  X  1  X  X  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1 X+1  X  1  1  1  1  X  0  1  0  X  1  0 X+1  0  X X+1  1  0  X  1  1  0  1  X  X  1  1 X+1 X+1  1  0  X X+1  0  X  X  0 X+1  1  1  0  0  X  1  1 X+1  0  1 X+1  1
 0  0  1  0  0  0  1  1  1  1 X+1  0  0 X+1  X  0 X+1  1  X X+1  0  1  X  1  0 X+1 X+1  0  1  1 X+1  1  1  0  X  0  1  1 X+1  X  1 X+1  1  X  0 X+1  0  X  X X+1  1  1  1 X+1  0  X  1  1  X  X X+1  X X+1  1  0
 0  0  0  1  0  1  1  0  1  X X+1  1  0  1  1  X  X  X X+1  1  1 X+1  X  X  0  0  1  0  1  0  1  0  0 X+1  1  0 X+1  0  0  X  1  1  1  0 X+1  1  1  0  1  1 X+1  X  X X+1  X  0 X+1  X  1  0  1  1  1  0 X+1
 0  0  0  0  1  1  0  1 X+1  X X+1 X+1  1  X  0  1  1  0 X+1  1 X+1  1  X  0  0  1 X+1  1  X  1  X  1  1  X  X X+1 X+1  0 X+1  1  X X+1  0  0  0  1 X+1 X+1 X+1  X  X X+1  0  0 X+1  0  1  X  0  0 X+1  0  1 X+1  X
 0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  X  0  X  0  0  0  0  X  X  X  X  X  X  0  X  0  X  X  0  X  0  X  0  0  X  X  X  0  0  X  0  0  0  0  X  X  0  0  X  X  0  X  X  X  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  0  0  X  0  X  0  X  X  0  0  X  0  0  X  0  X  X  0  0  X  X  0  X  X  X  X  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X  0  0  0  0

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+163x^54+481x^56+753x^58+868x^60+883x^62+908x^64+1037x^66+1011x^68+821x^70+599x^72+356x^74+190x^76+77x^78+35x^80+5x^82+3x^84+1x^90

The gray image is a linear code over GF(2) with n=130, k=13 and d=54.
This code was found by Heurico 1.16 in 9.6 seconds.